Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C8×Q8×D79 |
| Fitting | C8×Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C16×D79, #34198074, #34198210, … |
| maximal normal subgroup of | Q8⋊C16×D79, #34198074, #34198210, … |
| maximal quotient of | C8×C4⋊C4×D79, C8×#14579126, C8×Q8×Dic79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13429);